Patterns in melting snow and vapor deposited layers

We have observed a natural periodic pattern occurring in partially melted snow lying on the ground under certain atmospheric conditions. We explain this phenomenon quantitatively by considering heat flow through this layer coexisting in two phases (snow and water). Our model equations exhibit a range of patterns depending on the average density of snow. Strikingly similar patterns have been observed by Plass and co-workers in monolayer depositions of Pb on heated PbCu substrates. We argue that the physics of the two phenomena, differing in length scales by 7 orders of magnitude, is similar.